No ldiv!(x, A, b) on Bidiagonal matrices

General Usage
1

Suppose

using LinearAlgebra

n = 10
A = Bidiagonal(rand(n,n), :L)
F = factorize(A)
b = rand(n)
x = similar(b)

Then F === A and ldiv!(x, F, b) throws a no-method-error while ldiv!(F, b) is fine. Is this intended?